1WQC pattern scheduling to minimize the number of physical qubits

One of the quantum computing models without a direct classical counterpart is one-way quantum computing (1WQC). The computations are represented by measurement patterns in this model. One of the main downsides of the 1WQC model is the much larger number of qubits in a measurement pattern, compared to its equivalent in the circuit model. Therefore, proposing a method for optimally using the physical qubits to implement a measurement pattern is of interest, In a measurement pattern, despite a large number of qubits, the measured qubit is not needed after each measurement and can be used as another logical qubit. In this study, by using this feature and presenting an integer linear programming (ILP) model to change the ordering of a standard measurement pattern actions, the number of physical qubits required to implement that measurement pattern is minimized. In the proposed method, compared to the scheduling based on the standard pattern, the number of required physical qubits on benchmark circuits is reduced by 56.7% on average. Although the proposed method produces the optimal solution, one of the most important limitations of that and ILP-based methods, in general, is their high execution time and memory requirements, which grow exponentially with the increase of the problem size. In this study, an ILP model is proposed to minimize the number of physical qubits used to realize a measurement pattern by efficiently scheduling the operations and reusing the physical qubits. Due to its exponential complexity, the proposed method cannot be used for large measurement patterns whose solution can be conspired as future works.